A new software system for the state’s health insurance website passed its first key test this week, and a final decision on whether Massachusetts will run its own site or join the federal exchange will be made in early August, a top state official said.

Maydad Cohen, special adviser to the governor, told the Massachusetts Health Connector board Thursday morning that the new software from hCentive performed every task required by federal officials, and then some, in a Washington, D.C., demonstration Monday.

This success, he said in an interview afterward, leaves him increasingly but cautiously optimistic that the state will be able to employ the hCentive software when open enrollment starts Nov. 15.

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In the spring, the Health Connector abandoned its original, dysfunctional software, made by CGI, and adopted a “dual track” approach: working on a new system while simultaneously preparing to join the federal exchange, healthcare.gov.

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In a meeting Monday with Marilyn Tavenner, administrator of the US Centers for Medicare & Medicaid Services, officials demonstrated that software by the Virginia technology company hCentive can link to the federal “data hub,” the repository of Social Security and Internal Revenue Service data, a connection essential for verifying identities and income.

HCentive also ran through a complex enrollment scenario involving a couple who qualified for federal subsidies and had a child eligible for MassHealth.

The next stage of the hCentive product will be completed by July 30. If it passes another test in the first days of August, the state will stop its preparations to join the federal website and focus on completing hCentive’s system in time for the start of open enrollment. If it fails the August test, the state will join the federal exchange for next year but continue to try to develop its own system for 2016.

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Cohen also said that the hCentive program will be able to share information with MassHealth, the state’s Medicaid program, in a way that will enable most enrollees to apply through the Connector and determine eligibility in a “single front-door” process. As a result, people found eligible for Medicaid, instead of the subsidized private plans sold by the Connector, will not have to go through a second enrollment process.

The state is still negotiating its contract with Optum, the company hired to manage the dual-track project; hCentive is a subcontractor to Optum. Cohen said Thursday that the final cost is likely to be lower than the original estimate of $121 million, although no exact figure is yet available.

Asked what portion of that bill the state would pay, Cohen said, “Our sincere hope is that the federal government will pay for the entire amount.”

The Health Connector needed to retool and upgrade its website to meet the terms of the federal Affordable Care Act, but the system never worked properly from the day it opened last October, leaving people unable to determine whether they were eligible for government assistance. As a stopgap, people who thought they might be eligible for subsidies or Medicaid were allowed to enroll in Medicaid on a temporary basis through the end of this year.

Glen Shor, state secretary of administration and finance and Connector board chairman, told the board Thursday that 237,000 people had enrolled in the temporary Medicaid program and that the state had paid $138 million for their care by the end of June. He said that, so far, the costs of the temporary program have fallen within the Medicaid budget.

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The federal government will reimburse the state for 50 percent of the medical costs of the temporary enrollees, with the possibility some will qualify for 75 to 85 percent reimbursement, Shor added.

The early-August decision date is not a moment too soon for the state’s health insurers, who need time to develop their own systems for receiving enrollments and to communicate with members, said Lora Pellegrini, president and chief executive of the Massachusetts Association of Health Plans.

Amy Whitcomb Slemmer, executive director of the consumer advocacy group Health Care for All, said she was pleased with the developments.

“We are really encouraged that we’ll be able to have hCentive be the solution going forward,” she said. Having a state-based exchange is critical, Slemmer said, because the federal website cannot process the subsidies that Massachusetts provides in addition to the federal tax credits.